Is there a law in New York dictating that I have to meet my current boyfriend's ex-wife?

The ex cannot dictate who is around her daughter during the father's parenting time- only a judge can do that, and a judge will only set limitations if there is a danger of harm to the child. If you live with the boyfriend and the child and the ex has a good reason to suspect child abuse, she can start an investigation with child protective services and then a social worker will come to the house to meet you. But neither a social worker nor a judge can force you to meet the mother.  However, if you are involved in a serious relationship with this man, there will be school and other events at which the mother will inevitably be present- so eventually you'll have to meet her, and act in a pleasant and civil manner, which the father should do, as well.  I assume you don't have children. If you did, you'd understand that it is completely reasonable for a mother to want to meet a person who spends a lot of time with her daughter.  So just do it. By resisting meeting her mother, you're sending the wrong message to the daughter.